Third Capra Meeting on Radiation Reaction

Eric Poisson, University of Guelph

poisson@physics.uoguelph.ca

The Capra series of meetings on radiation reaction in curved spacetime
were initiated in 1998 by Patrick Brady. The first meeting was held at
Frank Capra's ranch in southern California, and the name stayed, even
though the location of the meeting has changed. (Frank Capra is the
famous movie director who made such films as ``It's a wonderful life''
and ``Mr. Deeds goes to town''. Capra had studied at Caltech before
going to Hollywood; he bequeathed his ranch to his alma mater, which
passed to Caltech upon his death.) The second meeting was held in
Dublin, Ireland, and was organized by Adrian Ottewill. This latest
installment was held at Caltech June 5-9, 2000, and was organized by
Lior Burko and Scott Hughes. Here I will present a rather broad
overview of the main issues discussed during the meeting, and
highlight just a few of the contributions. The complete proceedings
-- a copy of the slides presented by all the speakers -- can be
found at the meetings's web site: http://www.tapir.caltech.edu/~capra3/.
This series of meetings is concerned with the motion of a small mass
in a strong gravitational field. It is known that in the limit of
vanishing mass, the particle moves on a geodesic of the background
spacetime. Away from this limit, however, the motion in the background
is no longer geodesic, and can be described in terms of a
self-force. (In some sense, the motion is geodesic in the perturbed
spacetime, which consists of the background plus the perturbation
created by the particle. For a point particle, however, the
perturbation is singular at the particle's location, and careful
thought must be given to the removal of the singular part of the field,
which does not affect the motion. In flat spacetime, this subtraction
gives rise to the well-known half-retarded minus half-advanced
potential.) The main focus of the meeting was the practical
computation of this force.
While this problem raises many interesting issues of principle (such
as the removal of the singular part of the metric perturbation created
by a point particle), there is also a practical necessity. The
detailed modeling of gravitational waves produced by a solar-mass
compact object orbiting a massive black hole requires an accurate
representation of the orbital motion, which evolves as a result of
radiation loss. In the generic case involving a rapidly rotating black
hole, this evolution must be calculated on the basis of a
radiation-reaction force. Such sources of gravitational waves will be
relevant for the Laser Interferometer Space Antenna (LISA), a
space-borne detector designed to measure low-frequency waves (it has a
peak sensitivity at around 1 mHz).
The electromagnetic analogue to this problem was solved in 1960 by
DeWitt and Brehme [1], who derived a curved-spacetime expression
for the self-force acting on a point electric charge. The gravitational
self-force was obtained much more recently, first by Mino, Tanaka, and
Sasaki [2], and then by Quinn and Wald [3]. There is also a
similar force in the case of scalar radiation, which was calculated by
Quinn [4]. In all three cases the self-force is expressed as an
integral over the past world-line of the particle, and the integral
involves the nonsingular part of the retarded Green's function, which
has support inside the past light cone of the particle's current
position. The explicit evaluation of only this part of the Green's
function is challenging, however, and a good portion of the meeting
was devoted to this issue.
A plausible method for calculating the Green's function involves a
separation-of-variable approach made possible by the symmetries of the
black-hole spacetime. (Thus far, all calculations have been restricted
to the case of a Schwarzschild black hole). It is a simple matter to
derive and solve the ordinary differential equation that governs each
mode of the Green's function. The problem lies with the fact that the
sum over all modes doesn't converge. (This is essentially because the
individual modes do not distinguish between the singular and
nonsingular parts of the Green's function.) Amos Ori, Leor Barack, and
Lio Burko [5] have devised a way of regulating the mode sum, so
as to extract something meaningful. Their results for simple
situations involving scalar radiation were presented at the meeting,
and are extremely promising. A similar regularization method was used
by Carlos Lousto [6], who calculated the gravitational self-force
acting on a radially infalling particle in Schwarzschild spacetime.
Regularization was also exploited by Hiroyuki Nakano and Yasushi Mino
to calculate the gravitational self-force in the weak-field limit.
Insight into the self-force problem can be gained by adopting a more
local point of view, and focusing on the immediate vicinity of the
particle. Such an approach permits a clear identification of the
singular part of the particle's field, which can then be decomposed
into modes and subtracted from the full field. Such a strategy was
adopted by Steve Detweiler (in the gravitational case) and by Patrick
Brady (in the scalar case). A variation on this theme is to start with
the Mino poisson@physics.uoguelph.ca

**References:**

[1] B.S. DeWitt and R.W. Brehme, Ann. Phys. (NY) **9**, 220
(1960).

[2] Y. Mino, M. Sasaki, and T. Tanaka, Phys. Rev. D **55**,
3457 (1997).

[3] T.C. Quinn and R.M. Wald, Phys. Rev. D **56**, 3381
(1997).

[4] T.C. Quinn, gr-qc/0005030.

[5] See, for example, L.M. Burko, Phys. Rev. Lett. **84**,
4529 (2000), and L. Barack,
gr-qc/0005042.

[6] C.O. Lousto, Phys. Rev. Lett. **84**, 5251 (2000).